We propose the development of new theoretical methods to study site-specific mutagenesis and enzyme catalysis. These new theoretical methods build on two techniques recently developed, one involving molecular dynamics to calculate free energies for processes in solution; the other involving computer software for non-empirical ab initio quantum mechanics and molecular mechanics/dynamics. A gene-ralisation of the molecular dynamics/free energy approach will allow the determination of site specific mutagenesis effects on protein stability, binding and catalysis. Extensions of quantum/molecular mechanics method will allow a more efficient and accurate study of the process of enzyme catalysis. Application of these two approaches will be made on the interactions of tyrosine tRNA synthetase and its mutants with tyrosyl-AMP and the transition state complex between ATP and tyrosine, the system where there is the most extensive experimental work by Fersht and co-workers on site specific mutagenesis effects and catalysis. The aspartyl proteases are an appropriate system for applications of both free energy technique and combined quantum/molecular mechanics technique. The first method may allow optimum design of inhibitors for renin which may have importance to treatments of hyper tension. The second method will allow an assessment of the reality of many proposed mechanism of peptide cleavage by the aspartyl proteases.